A polygon is simple if it is a closed chain of straight line segments that do not self-intersect. Given a finite set P of input points in the Euclidean plane, the search for a simple polygon with vertex set P is a very well-known and studied computational problem, referred to as the simple polygonization. Its optimization version, that requires to find a simple polygon having either minimum or maximum area, is known to be NP-hard. Moreover, no bounded approximation algorithm is known for the minimization flavor, while the maximization one admits an algorithm guaranteeing $\frac{1}{2}$ worst-case approximation ratio. In this work, we design a new algorithm to practically attack both the optimization problems, based on the genetic paradigm. We demonstrate its effectiveness through an extensive experimental evaluation that employs a reference test-bed set of input instances.

如果多边形是不自相交的直线段的闭合链，则它很简单。给定欧几里得平面中输入点的有限集合P，以顶点集合P寻找简单多边形是众所周知的且已研究的计算问题，称为简单多边形化。它的优化版本需要找到一个具有最小或最大面积的简单多边形，这被称为NP-hard。此外，对于最小化风格，没有已知的有界逼近算法，而最大化则允许一种算法来保证$\frac{\mathrm{1个}}{\mathrm{2个}}$最坏情况下的近似率。在这项工作中，我们基于遗传范式设计了一种新的算法，用于实际攻击这两个优化问题。我们通过广泛的实验评估来证明其有效性，该评估采用了输入实例的参考测试台集。